Problem: Solve for $x$ and $y$ using substitution. ${-6x+3y = 12}$ ${x = -3y-9}$
Solution: Since $x$ has already been solved for, substitute $-3y-9$ for $x$ in the first equation. ${-6}{(-3y-9)}{+ 3y = 12}$ Simplify and solve for $y$ $18y+54 + 3y = 12$ $21y+54 = 12$ $21y+54{-54} = 12{-54}$ $21y = -42$ $\dfrac{21y}{{21}} = \dfrac{-42}{{21}}$ ${y = -2}$ Now that you know ${y = -2}$ , plug it back into $\thinspace {x = -3y-9}\thinspace$ to find $x$ ${x = -3}{(-2)}{ - 9}$ $x = 6 - 9$ ${x = -3}$ You can also plug ${y = -2}$ into $\thinspace {-6x+3y = 12}\thinspace$ and get the same answer for $x$ : ${-6x + 3}{(-2)}{= 12}$ ${x = -3}$